Non-global logarithms up to four loops at finite-N$_c$ for V/H+jet processes at hadron colliders

We extend our previous work [1] on calculating non-global logarithms in $e^+ e^-$ annihilation to Higgs/vector boson production in association with a single hard jet at hadron colliders. We analytically compute non-global coefficients in the jet mass distribution up to four loops using the anti-k$_t$ jet algorithm. Our calculations are performed in the eikonal approximation, assuming strong energy ordering for the emitted gluons, thus capturing only the leading logarithms of the distribution. We compare our analytical results with the all-orders large-N$_c$ numerical solution. In general, the gross features of the non-global logarithm distribution observed in the $e^+ e^-$ case remain valid for the V/H+jet processes.